量子群U_q(f(K))的局部有限子代数的稳定理想

利用量子群U=U_q(f(K))的表示理论及其局部有限子代数F(U)的子模结构,证明了U_q(f(K))的局部有限子代数F(U)的任一非零理想均可由若干个具有不同权的最高权向量的和生成.     

Young表与$textrm{U}_{q}(mathrm{osp}(1|2n))$的晶体基

设 $U_q(mathrm{osp}(1|2n))$是对应Lie超代数$mathrm{osp}(1|2n)$的量子包络超代数. 利用满足一定条件的半标准Young表, 给出有限维既约$U_q(mathrm{osp}(1|2n))$模晶体图的实现 . 建立晶体图张量积分解的广义Littlewood-Richardson法则.     

量子代数wsl_q(2)上的伴随作用

本文证明了量子代数wslq(2)在左伴随作用下是其自身上的拟模代数,并研究了wslq(2)的局部有限子模(?)(wslq(2))的子模结构．     

由H\"{o}rmander向量场构成的抛物方程的 $W_{ast}^{1,p}$ 正则性

设 $X_{1},cdots ,X_{q} (q相似文献   

vspace{-1cm}$W(2,boldsymbol{n})$和$H(2,boldsymbol{n})$的$p$-特征标高度为$2$的不可约模的分类$^{}$

研究$p$-!!特征标高度等于$2$的$W(2,boldsymbol{n})$和$H(2,boldsymbol{n})$ 的不可约表示, 给出了当 $p$-!!特征标$chi $的 高度等于$2$时,$L=X(2,boldsymbol{n})$, $X=W,H$ 的不可约$L$-!!模同构类代表元集合.     

系数在模李超代数~$W(m,3,underline{1})$ 上的~$frak{gl}(2,mathbb{F})$ 的一维上同调

研究了系数在模李超代数~$W(m,3,underline{1})$上的~$frak{gl}(2,mathbb{F})$ 的一维上同调, 其中~$mathbb{F}$是一个素特征的代数闭域且~$frak{gl}(2,mathbb{F})$是系数在~$mathbb{F}$ 上的~$2times 2$ 阶矩阵李代数.计算出所有~$frak{gl}(2,mathbb{F})$到模李超代数~$W(m,3,underline{1})$ 的子模的导子和内导子.从而一维上同调~$textrm{H}^{1}(frak{gl}(2,mathbb{F}),W(m,3,underline{1}))$可以完全用矩阵的形式表示.     

旗传递点本原且基柱为${rm PSL}_n(q)$的$(v,k,4)$-对称设计

若$cal D$为一个非平凡旗传递点本原对称$(v,k,4)$设计, 其基柱为${rm PSL}_n(q)$且$Gleq {rm Aut}(cal D)$. 那么, $cal D$ 必为$2$-$(15,8,4)$设计且${rm Soc}(G)={rm PSL}_2(9)$.     

关于代数微分方程(f')~n=R(z,f)的亚纯解

在本文中,我们首先考虑了具有理系数的代数微分方程（ｆ＇）ｎ＝Ｒ（ｚ,ｆ）亚 纯解的个数估计问题,并举例说明所得结果是精确的．其次,我们运用 Ｎｅｖａｎｌｉｎｎａ值 分布论,讨论了具亚纯系数的典型代数微分方程（ｆ＇）３＝ａ０（ｆ－ τ１）２（ｆ－ τ２）２（ｆ－ τ３）２ 的可分解亚纯解．文中的结果推广或改进了高仕安［１］,Ｇｕｎｄｅｒｓｅｎ Ｇ．和ＬａｉｎｅＩ［２］以 及何育赞, ＬａｉｎｅＩ．［３－５］等人的工作．     

关于代数微分方程(f')~n=R(z,f)的亚纯解

在本文中,我们首先考虑了具有理系数的代数微分方程（ｆ＇）ｎ＝Ｒ（ｚ,ｆ）亚 纯解的个数估计问题,并举例说明所得结果是精确的．其次,我们运用 Ｎｅｖａｎｌｉｎｎａ值 分布论,讨论了具亚纯系数的典型代数微分方程（ｆ＇）３＝ａ０（ｆ－ τ１）２（ｆ－ τ２）２（ｆ－ τ３）２ 的可分解亚纯解．文中的结果推广或改进了高仕安［１］,Ｇｕｎｄｅｒｓｅｎ Ｇ．和ＬａｉｎｅＩ［２］以 及何育赞, ＬａｉｎｅＩ．［３－５］等人的工作．     

有限维模李超代数W(m,n,l,(t))的θ-型导子与导子超代数

In this paper F always denotes a field of characteristic P＞2.We construct the finitedimensional modular Lie superalgebra W(m,n,l,(t))over a field F,define θ-type derivation and determine the derivation superalgebra of w(m,n,l,(t)).     

A Combinatorial Character Formula for Some Highest Weight Modules

We give a combinatorial formula for the weight multiplicities of some infinite-dimensional highest weight (n)-modules. Our proof, which does not rely on Kazhdan–Lusztig combinatorics, uses a reduction to finite characteristics. The character formula for the corresponding modular representations, which has been computed in a 1997 preprint by the authors, is based on a dual pair which has no obvious counterpart in characteristic zero.     

Derivations of generalized Weyl algebras

A class of the associative and Lie algebras A[D] = A F[D] of Weyl type are studied, where A is a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] is the polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A such that A is D-simple. The derivations of these associative and Lie algebras are precisely determined.     

Structure of cohomology modules of linear bundles overG/B and weak ordering on the weyl group

We consider the cohomologyG-modules of linear bundles over the flag manifoldG/B over an algebraically closed field of prime characteristic. We study the structure of submodules of these modules and their homomorphisms. Translated fromMaternaticheskie Zametki, Vol. 62, No. 2, pp. 163–168, August, 1997. Translated by S. K. Lando     

有序拓扑向量空间中的共鸣定理

本文研究有序拓扑向量空间中非线性映照的共鸣定理．对于取值于有序拓扑向量空间中的映照，利用序关系，引入了一类广泛的非线性映照．对于这类非线性映照，应用纲理论，并给出了关于点态序有界蕴涵一致序有界的共鸣定理．     

Dominant K-theory and integrable highest weight representations of Kac-Moody groups

We give a topological interpretation of the highest weight representations of Kac-Moody groups. Given the unitary form G of a Kac-Moody group (over C), we define a version of equivariant K-theory, KG on the category of proper G-CW complexes. We then study Kac-Moody groups of compact type in detail (see Section 2 for definitions). In particular, we show that the Grothendieck group of integrable highest weight representations of a Kac-Moody group G of compact type, maps isomorphically onto , where EG is the classifying space of proper G-actions. For the affine case, this agrees very well with recent results of Freed-Hopkins-Teleman. We also explicitly compute for Kac-Moody groups of extended compact type, which includes the Kac-Moody group E₁₀.